7. DISCUSSION AND IMPLICATIONS
7.1 A NSWERS TO R ESEARCH Q UESTIONS
The following discussion summarizes the proposed answers to the research questions posed in the introductory section of this dissertation.
RQ1: What is the difference between control interrelationships and cue interrelationships?
This dissertation proposes that control interrelationships do not always translate directly to cue interrelationships and that, in fact, they are two different concepts.
Control interrelationships are described in audit regulation and can be defined by how controls interact in their relation to risk (see discussion under section 3.5.2). Since, in auditing, risk is conceptualized through the audit risk model, it is furthermore reasonable to state that control interrelationship concepts are based on some form of continuous risk scale – typically a percentage point risk scale.
Cue interrelationships, however, are more generic in that they can be defined by how cues interact in their relation to a criterion (i.e., the state of an external reality) (see figure 26 below) (Libby 1981, p8, item B3). While control interrelationships are tied to a risk scale, the general construct of cue interrelationships may be tied to any kind of scale.
Figure 26: Cue Interrelationships (Lens Model Environment)
Criterion Cue set
Cue A Cue B Cue C
Cue interrelationships True
criterion level
A sufficient argument for control interrelationships and cue interrelationships being two different concepts is that a change in the judgment response scale may change cue interrelationships even if controls, and thus control interrelationships, remain the same (see discussion under section 3.5.2). For example, if controls are independent and the judgment response scale is continuous, then cues are independent. If controls remain unchanged, but the judgment response scale changes to binary, then the cues will be completely-dependent, since all cues are necessary for a positive judgment (see discussion under section 3.5.2 and discussion of RQ2 and RQ3 below). In general, when controls serve as cues, a change in the judgment response scale may cause cue interrelationships to change (i.e., even though the cues (controls) remain constant). Control interrelationships are therefore one of the determinants of cue interrelationships, and they are therefore two different concepts (see figure 27 below and further discussion under the response to RQ6 below):
Figure 27: Model of Determinants of Cue Interrelationships
Control Interrelationships “COI”
Cue Interrelationships
“CUI”
Criterion Scale “CS”
Judgment Response Scale “JRS”
Note that it is not suggested that controls and cues are two different constructs; in audit judgment research, controls may serve as operationalizations of cues. However, the interrelationships are two different constructs, and it is the interrelationships that are the independent variables in this dissertation.
RQ2: What is the nature and range of variation in the control interrelationship variable?
In auditing, risk is conceptualized through the audit risk model. It is therefore reasonable to state that control interrelationship concepts are based on some form of continuous scale – typically a percentage point risk scale. This dissertation therefore proposes a framework
where control interrelationships are a function of how controls interact in their relationship to risk (see figure 28 below).
Figure 28: Control Interrelationships (Lens Model Environment Side)
Criterion Cue set
Control A
The range of variation in control interrelationships spans from completely-dependent to substitutable (see figure 29 below).
The range of variation in control interrelationships has five sections:
1. Completely dependent controls, where a control only has an effect if all other controls are present (i.e., all controls must be present if any effect is to occur; all controls are necessary)
2. Amplifying controls, where the effect of two controls combined is larger than the sum of the two individual control effects
3. Independent controls, where each control’s effect is independent of the level (i.e., presence/absence) of other controls
Control B Control C True
risk level Control interrelationships
Figure 29: Cue Interrelationship Continuum
(3) Independent
(1) Completely-Dependent (5) Substitutable
(2) Amplifying (4) Compensating
4. Compensating controls, where the effect of two controls combined is smaller than the sum of the two individual control effects
5. Substitutable controls, where controls have the same individual effect and where the effect of two controls combined is the same as the individual contribution of one control (i.e., controls can substitute for each other, but they do not add incremental effect if another control is already present)
The control interrelationship continuum can furthermore be described mathematically by use of functions. Assume that “y” represents the risk criterion level and that “y” is a function of control cues “cBiB”:
Let y = f(cBiB), where there are two cues (i=1,2) and cues take on the values 0 or 1 (cBi B= 0,1) and
0 = 0/100 ≤ f(cB1B,cB2B) ≤ 100/100 = 1 f(0,0) = 0 for all functions
This provides the following control interrelationship functions (see table 17 below):
Table 18: Mathematical Representation of Control Interrelationship Functions Control interrelationship Mathematical Function Description
1. Completely-dependent
f(1,0) = f(0,1) = 0, and f(1,1) > 0 Complete positive interrelationship 2. Amplifying 0 < f(0,1) + f(1,0) < f(1,1)
0 < f(1,0), 0 < f(0,1)
Partial positive interrelationship
3. Independent 0 < f(0,1) + f(1,0) = f(1,1) 0 < f(1,0), 0 < f(0,1)
No interrelationship
4. Compensating 0 < f(1,1) < f(0,1) + f(1,0) 0 < f(1,0), 0 < f(0,1)
Partial negative interrelationship
5. Substitutable 0 < f(1,0) = f(0,1) = f(1,1) Complete negative interrelationship
RQ3: What is the nature and range of variation in the cue interrelationship variable?
This dissertation proposes a framework where cue interrelationships are a function of how cues interact in their relationship to a general criterion. While control interrelationships are tied to a risk scale, the general construct of cue interrelationships may be tied to any kind of scale (see figure 30 below).
Figure 30: Cue Interrelationships (Lens Model Environment Side)
Criterion Cue set
Cue A
The range of variation in cue interrelationships is identical to what is described for control interrelationships under RQ2 above:
1. Completely-dependent 2. Amplifying
3. Independent 4. Compensating 5. Substitutable
RQ4a: What is the nature and range of variation in the judgment response scale variable?
This dissertation proposes that the judgment response scale as a task characteristic is the nature of the auditors’ judgment response (e.g., risk, likelihood, impact) and the range of variation is the number of judgment response options the judge has available for a given judgment task. In the simplest form, a judgment response scale is binary (e.g., yes/no, effective/deficient, acceptable/unacceptable). As more response options become available, the scale approaches continuity (see figure 31 below). It is reasonable to assume that in many practical audit judgment situations the continuous response scale is approximated in the form of percentage point judgments (e.g., the audit risk model).
Cue B Cue C
Cue interrelationships True
criterion level
URQ4b: What is the nature and range of variation in the criterion scale variable?
The criterion is the true state of the reality that the judge is making a judgment about (typically an event or state). Although the level of the criterion is unknown to the judge, the nature and range of the criterion scale is known through knowledge of the judgment response scale (e.g., the judge knows that the nature of the criterion is control risk and that the range is a percentage scale since this is what he is asked to make a judgment about, but he does not know that the true level of control risk is e.g., 27%). Since the nature and range of the criterion are determined by the judgment response scale, the same scale also applies (i.e., the same scale as described under RQ4a above).
URQ5: What forms of judgment policies and models are relevant in auditors internal control judgments?
A judgment policy is the manner in which cues are weighted and combined by the judge when making a judgment. This can be illustrated by the judgment side of the Lens Model (see figure 32 below):
2
Continuous Figure 31: Judgment Response Scale: Number of Response Options
Control Risk 100 Effective/Deficient
∞
A judgment model is a mathematical representation of a judgment policy. In policy capturing, a judgment model is a paramorphic (i.e., surface) representation of the judgment policy. The range of relevant judgment policies and models in internal control judgment tasks is proposed to include:
UCompensatory, additive, linear models:
• Linear model
UCompensatory, additive, nonlinear models:
• Compensatory form ordinal model
• Amplifying form ordinal model
UNoncompensatory, nonadditive, nonlinear models:
• Conjunctive model
• Disjunctive model
URQ6: How should control interrelationships and the judgment response scale affect cue interrelationships and judgment policies?
This dissertation suggests the following normative propositions:
Control A Control B Control C
Judgment Information cue set
Figure 32: Lens Model for Control Risk Judgment (Lens Model Judgment Side)
Auditor judgment of
control risk
%-level
Cue weighting and cue combination
P1: A normatively appropriate functional form of the judgment policy (FFJP) can be derived from studying cue interrelationships (CUI).
P2: Cue interrelationships (CUI) can be derived from studying control interrelationships (COI) and the judgment response scale (JRS).
P3: The judgment response scale (JRS) determines the criterion scale (CS).
The propositions are illustrated in the conceptual model below (see figure 33 below):
The mechanism through which the judgment response scale alters cue interrelationships is proposed to be as follows:
• A change in the judgment response scale (JRS) implies a change in the criterion scale (CS)
• The criterion scale (CS) and control interrelationships (COI) determine cue interrelationships (CUI)
• Cue interrelationships (CUI) determine the functional form of the judgment policy (FFJP)
The following normative relationships are proposed:
UContinuous judgment response scale COI
JRS
FFJP CUI
Figure 33: Conceptual Model in this Dissertation
CS
1. If controls are completely-dependent and the judgment response scale is continuous, then cues are completely dependent and a conjunctive judgment policy is appropriate.
2. If controls are compensating and the judgment response scale is continuous, then cues are compensating and a compensatory form ordinal judgment policy is appropriate.
3. If controls are independent and the judgment response scale is continuous, then cues are independent and a linear judgment policy is appropriate.
4. If controls are amplifying and the judgment response scale is continuous, then cues are amplifying and an amplifying form ordinal judgment policy is appropriate.
5. If controls are substitutable and the judgment response scale is continuous, then cues are substitutable and a disjunctive judgment policy is appropriate.
Binary judgment response scale:
1. If controls are substitutable and the judgment response scale is binary, then cues are substitutable (i.e., individually sufficient) and a disjunctive judgment policy is appropriate.
2. If controls are independent, amplifying, compensating or completely-dependent, and the judgment response scale is binary, then cues are completely-dependent (i.e., not individually sufficient) and a conjunctive judgment policy is appropriate It can be noted that cues that are independent, compensating or amplifying in continuous judgment tasks are either (1) individually sufficient in binary judgment tasks (and thus become substitutable), or (2) not individually sufficient in binary judgment tasks (and thus become completely dependent). This can also be understood as sufficient (i.e., substitutable) or necessary (i.e., completely dependent) conditions for binary judgment outcomes. In general, independent, amplifying and compensating cues do therefore not, by definition, exist in binary judgment tasks.
RQ7: How do control interrelationships and the judgment response scale affect judgment policies?
This dissertation makes the following descriptive proposition:
P4: Auditors make judgments by using judgment policies that have normatively appropriate forms of cue integration given the cue interrelationships that result from control interrelationships and the judgment response scale.
RQ7 is the empirical equivalent to the normative research question in RQ6. It is hypothesized that auditors make judgments by using judgment policies that are consistent with what is normatively proposed in RQ6.
The conducted experiment provides the following evidence. For the continuous judgment response scale, findings are reported at the nomothetic level (i.e., aggregate group level). For the binary judgment response scale, findings are reported at the ideographic level (i.e., individual level):
Continuous judgment response scale
1. H1a: If controls are completely-dependent and the judgment response scale is continuous, then cues are completely dependent and a conjunctive judgment policy is appropriate. The aggregate group level judgment model is consistent with the use of such a judgment policy.
2. H2a: If controls are substitutable and the judgment response scale is continuous, then cues are substitutable and a disjunctive judgment policy is appropriate. The aggregate group level judgment model is consistent with the use of such a judgment policy.
3. H3a: If controls are independent and the judgment response scale is continuous, then cues are independent and a linear judgment policy is appropriate. The aggregate group level judgment model is consistent with the use of such a judgment policy.
4. H4a: If controls are compensating and the judgment response scale is continuous, then cues are compensating and a compensatory form ordinal judgment policy is
appropriate. The aggregate group level judgment model is consistent with the use of such a judgment policy.
5. H5a: If controls are amplifying and the judgment response scale is continuous, then cues are amplifying and an amplifying form ordinal judgment policy is appropriate. The aggregate group level judgment model is not consistent with the use of such a judgment policy. However, in this experiment a judgment model consistent with a linear judgment policy was, on average, used by participants.
One potential explanation for this finding is that participants may not have perceived the cue interrelationship treatment as intended (see detailed discussion of H4a in the results section).
Binary judgment response scale:
1. H1b: If controls are completely-dependent and the judgment response scale is binary, then cues are completely-dependent (i.e., not individually sufficient) and a conjunctive judgment policy is appropriate and used. Analysis of individual judgment policies showed that most auditors (i.e., 20 out of 21) had a judgment model consistent with the hypothesized judgment policy. The likelihood of observing 20 out of 21 participants using the hypothesized judgment policy versus any other judgment policy being due to randomness is <0.001. Results are therefore consistent with H1b.
2. H2b: If controls are substitutable and the judgment response scale is binary, then cues are substitutable (i.e., individually sufficient) and a disjunctive judgment policy is appropriate and used. Analysis of individual judgment policies showed that most auditors (i.e., 18 out of 21) had a judgment model consistent with the hypothesized judgment policy. The likelihood of observing 18 out of 21 participants using the hypothesized judgment policy versus any other judgment policy being due to randomness is <0.001. Results are therefore consistent with H2b.
3. H3b: If controls are independent and the judgment response scale is binary, then cues are completely-dependent (i.e., not individually sufficient) and a conjunctive judgment policy is appropriate and used. Analysis of individual judgment policies
showed that most auditors (i.e., 18 out of 21) had a judgment model consistent with the hypothesized judgment policy. The likelihood of observing 18 out of 21 participants using the hypothesized judgment policy versus any other judgment policy being due to randomness is <0.001. Results are therefore consistent with H3b.
4. H4b: If controls are compensating and the judgment response scale is binary, then cues are completely-dependent (i.e., not individually sufficient) and a conjunctive judgment policy is appropriate and used. Analysis of individual judgment policies showed that the majority of auditors (i.e., 13 out of 21, or 62%) had a judgment model consistent with the hypothesized judgment policy. The likelihood of observing 13 out of 21 participants using the hypothesized judgment policy versus any other judgment policy being due to randomness is <0.094. Results are therefore marginally supportive of H4b. One potential explanation for the finding on compensating controls being only marginally supportive of H4b is that participants may have assessed the controls to be sufficiently compensating to be substitutable in the binary judgment, and thus may have not absorbed the intended cue interrelationship treatment (see further discussion in section 6.3.4).
5. H5b: If controls are amplifying and the judgment response scale is binary, then cues are completely-dependent (i.e., not individually sufficient) and a conjunctive judgment policy is appropriate and used. Analysis of individual judgment policies showed that most auditors (i.e., 15 out of 21) had a judgment model consistent with the hypothesized judgment policy. The likelihood of observing 15 out of 21 participants using the hypothesized judgment policy versus any other judgment policy being due to randomness is <0.006. Results are therefore consistent with H5b.
Overall it seems that auditors generally make judgments by using normatively appropriate judgment policies given the cue interrelationships that result from control interrelationships and the judgment response scale. In this study, the task characteristics of amplifying cues and a continuous judgment response scale, was an exception to this general finding: On average auditors exhibited a linear judgment model instead of the hypothesized amplifying form ordinal model. It is, however, not unlikely that the exception was due to participants
not absorbing the cue interrelationship treatment as intended. Furthermore findings for compensating controls and a binary judgment response scale are only marginally supportive of the hypothesized judgment policy.